Calculate Stokes drag on a sphere and its terminal settling velocity from radius, viscosity, speed and densities.
Low-Reynolds-number model only: Stokes’ law is valid for slow, laminar flow around a smooth sphere (Re below about 1); fast or large particles need drag-coefficient methods.
Stokes drag force (µN)
How to use this tool
Use millimetres; drag scales linearly with radius, while terminal velocity scales with radius squared.
Use milliPascal-seconds: water is about 1, honey is thousands.
Velocity gives the drag force; the density difference drives terminal settling.
Trust Stokes’ law only when Re is below about 1; larger values mean turbulence and a different drag regime.
Formula & worked example
A 1 mm sphere in water (η = 1 mPa·s) moving at 0.01 m/s feels drag = 6π x 0.001 x 0.001 x 0.01 = 1.885 x 10⁻⁷ N (0.1885 µN); with densities 2,500 and 1,000 kg/m³ its terminal velocity is 3.269 m/s, though Re = 20 warns this case is outside the strict Stokes regime.
Limitations — read this before you rely on it
Strictly valid only for Re below about 1, smooth spheres and laminar flow. The worked terminal-velocity example itself exceeds that range, which is why the Reynolds number is shown: use drag-coefficient methods for fast, large or non-spherical particles.
Frequently asked questions
Weight grows with volume (radius cubed) while drag grows with radius, so the balance velocity grows with radius squared.
The density difference goes negative and the terminal velocity is upward: the particle rises instead of settling.
The ratio of inertial to viscous forces. Low Re means smooth, viscous-dominated flow where Stokes’ law holds.
Yes: Stokes’ law is for spheres. Irregular grains settle more slowly and need shape corrections.
Sedimentation analysis, aerosol behaviour, blood-cell settling, inkjet droplets and microfluidics.